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<p>We consider a nonlinear Robin problem driven by a differential operator with unbalanced growth and a reaction which exhibits the competing effects of a parametric concave (sublinear) term and of a convex (superlinear) term. Using the Nehari method, we show that for all small values of the parameter, the problem has two bounded, ground state (least energy) solutions. In the process of the proof, we establish some auxiliary results which are of independent interest.</p>

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Ground State Solutions for Robin Concave–Convex Problems with Unbalanced Growth

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月20日

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  • Peng Jin,
  • Nikolaos S. Papageorgiou,
  • Vicenţiu D. Rădulescu

摘要

We consider a nonlinear Robin problem driven by a differential operator with unbalanced growth and a reaction which exhibits the competing effects of a parametric concave (sublinear) term and of a convex (superlinear) term. Using the Nehari method, we show that for all small values of the parameter, the problem has two bounded, ground state (least energy) solutions. In the process of the proof, we establish some auxiliary results which are of independent interest.